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“Untitled (OctSquare)” © 2005

This is a “compound” tiling: two different symmetries, in this case octagonal (8-fold) and quadrilateral (4-fold) are used to fill the plane.  Each locally symmetric element is filled with a fractal exhibiting the same symmetry so that everything “fits” together nicely.  Much fractal art is occupied with finding visually interesting places in the fractal microcosm.  I’m more interested in using fractals as parts of structured wholes, tiling the plane with them, e.g.